1. Field of the Invention
The present invention relates to the determination of sub-spaces of facial variations.
2. Related Art
Facial variation can be conceptually divided into a number of ‘functional’ sub-spaces; types of variation which reflect useful facial dimensions [M. J. Black, D. J. Fleet, and Y. Yacoob. A framework for modelling appearance change in image sequences. 6th ICCV, pages 660-667, 1998.]. A possible selection of these face-spaces is: identity, expression (here including all transient plastic deformations of the face), pose and lighting. Other spaces may be extracted, the most obvious being age. When designing a practical face-analysis system, one at least of these sub-spaces must be isolated and modelled. For example, a security application will need to recognise individuals regardless of expression, pose and lighting, while a lip-reader will concentrate only on expression. In certain circumstances, accurate estimates of all the sub-spaces are needed, for example when ‘transferring’ face and head movements from a video-sequence of one individual to another to produce a synthetic sequence.
Although face-images can be fitted adequately using an appearance-model space which spans the images, it is not possible to linearly separate the different sub-spaces [S. Duvdevani-Bar, S. Edelman, A. J. Howell, and H. Buxton. A similarity-based method for the generalisation of face recognition over pose and expression. 3rd Face and Gesture, pages 118-123, 1998]. This is because the sub-spaces include some degree of overlap (for example, a ‘neutral’ expression will actually contain a low-intensity expression).